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Deciding game invariance

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  • Additional Information
    • Publication Information:
      Academic Press
    • Publication Date:
      2017
    • Collection:
      University of Liège: ORBi (Open Repository and Bibliography)
    • Abstract:
      peer reviewed ; In a preivous paper, Duchêne and Rigo introduced the notion of invariance for take-away games on heaps. Roughly speaking, these are games whose rulesets do not depend on the position. Given a sequence S of positive tuples of integers, the question of whether there exists an invariant game having S as set of P -positions is relevant. In particular, it was recently proved by Larsson et al. that if S is a pair of complementary Beatty sequences, then the answer to this question is always positive. In this paper, we show that for a fairly large set of sequences (expressed by infinite words), the answer to this question is decidable.
    • ISSN:
      0890-5401
      1090-2651
    • Relation:
      urn:issn:0890-5401; urn:issn:1090-2651; https://orbi.uliege.be/handle/2268/205740; info:hdl:2268/205740; https://orbi.uliege.be/bitstream/2268/205740/1/final.pdf
    • Accession Number:
      10.1016/j.ic.2017.01.010
    • Online Access:
      https://doi.org/10.1016/j.ic.2017.01.010
      https://orbi.uliege.be/handle/2268/205740
      https://orbi.uliege.be/bitstream/2268/205740/1/final.pdf
    • Rights:
      open access ; http://purl.org/coar/access_right/c_abf2 ; info:eu-repo/semantics/openAccess
    • Accession Number:
      edsbas.BBB8543F